It has been shown by H. Nyquist that the speed of transmission over an ideal low-pass network cannot exceed two data pulses per hertz of passband, and that this theoretical limit could be approached by a transmission channel whose overall behaviour for data pulses is like that of a low-pass filter of linear phase characteristic and gradual cutoff. Thus, when it is desired to transmit data at a high binary rate, it becomes necessary firstly to reduce the transmission speed for transmission purposes by replacing the binary data with multivalent symbols, and secondly to bring the characteristics of the link used for the transmission as close as possible to those of a low-pass filter with a linear phase characteristic and gradual cutoff, by means of a shaping filter, optionally by means of modulation, and by correcting the distortion applied to the useful band by the link as set up for the transmission.
In practice, binary data streams for transmission are transformed either into a string of real multivalent symbols at a lower rate for transmission over a single channel, or else into a string of pairs of real multivalent symbols at a lower rate for simultaneous transmission over two inpendent channels in quadrature. The first case is encountered particularly in baseband transmission systems, or in systems using single or residual sideband amplitude modulation, while the second case is encountered in data transmissions using amplitude modulation of two carriers in quadrature, or in similar systems such as transmission by phase jumps between four or eight states or using combined phase and amplitude modulation. Where two channels in quadrature are used, it is possible to reduce the second case to the first by considering the two components of a pair of symbols as the real part and the imaginary part of a complex symbol, and by substituting complex quantities for the real quantities used in calculations performed by the first case. Conversely, a study of the first case can be assimilated to one of the second by associating a quadrature channel to the single channel. A signal derived from that transmitted over the single channel is applied to the quadrature channel, this signal is usually the Hilbert transform of the single channel signal. For these reasons, it is customary to represent a data transmission signal in complex form.
The distortion suffered in the useful band comprises both distortion of slowly varying characteristics of the transmission channel, in the form of amplitude distortion and of group propagation delay distortion, and also distortion of somewhat more rapidly varying characteristics in the form of phase noise distortion. Distortion correction is performed on the multivalent symbols. When modulation is present, it may also be performed on the received signal in its passband before demodulation.
Amplitude distortion and group propagation delay distortion in the transmission channel are corrected by means of a filter which, in the useful band, has transmission characteristics that are the inverse of those of the transmission channel, whereby the overall response in said band is flat in amplitude and linear in phase. For this purpose, it is standard practice to use linear self-adaptive equalizers based on K. E. Kalmann's time domaine transversal filter using coefficients that are controlled to minimize the error between received symbols and their exact values or their estimated values. Such equalizers are automatically matched to the characteristics of the transmission channel during a setting up period when the data stream is replaced by a test sequence known at the receiving end, and thereafter they continue to adapt to the slowly varying characteristics of the transmission channel during data transmission.
One self-adaptive linear equalizer of the above-mentioned type and used in conjunction with a single channel, after demodulation where appropriate, comprises a time domain transversal filter having a delay line with intermediate taps separated by the unit of time which separates two successive symbols at transmission, and whose coefficients are constantly being adjusted by feedback control loops which tend to minimize the mean square error using a gradient algorithm defined by a linear equation of first order differences between real magnitudes.
The abovementioned self-adaptive linear equalizer is suitable for a single channel but there exists a complex version suitable for two channels in quadrature. The complex version can be deduced from the simple version by the "complex/real" correspondence mentioned above, and may be considered as comprising four time domain transversal filters arranged in a trellis configuration, pairs of said filters having the same sets of coefficients, and their outputs being connected in pairs, one pair via a subtractor and the other via an adder. The feedback control loops tending to minimize the mean square error use a gradient algorithm defined by the same linear equation of first order differences, but this time between complex magnitudes.
The relative importance of phase noise increases with transmission rate. In particular, phase noise on the telephone network is not a hindrance for conversations where data is transmitted at a low rate (1,200 bits/s), but it becomes more troublesome for transmission of data at higher rates (4,800 bits/s and above). Phase noise may have various components:
a drift in frequency, for example due to modulation followed by demodulation using carriers that are not synchronized; PA1 a constant phase shift; PA1 a periodic phase shift varying at mains frequency or one of its harmonics, such as is encountered particularly when using cables with carrier waves; and PA1 a random phase shift occuring at low frequency with respect to the bandwidth of the channel. PA1 the phase error is estimated twice; PA1 two complex exponentials corresponding to two correction angles are generated; and PA1 two complex multiplications are performed to obtain two phase corrections. There is thus considerable complication in the implementation of a phase noise correction circuit. PA1 a phase shift angle generator having an incrementation input and providing the phase shifter circuit with the value of a phase shift angle updated at the rate at which the symbols are received; PA1 a phase error detector providing the value of the phase error between the received and the estimated symbols appearing at the terminals of the decision circuit, likewise at the rate at which the symbols are received; and PA1 a filter interposed between the output of the phase error detector and the incrementation input of the phase shift angle generator, the said filter having a transfer function expressed as follows using the z transform: ##EQU2## where a is a constant approximately equal to 0.92
Phase noise can be considered as being derived from variations in the characteristics of the transmission channel. However, except for its DC and very low frequency components, phase noise cannot be eliminated by the linear self-adaptive equalizers used to correct amplitude distortion and group propagation delay distortion of the transmission channel since such filters converge too slowly. Indeed, said correction requires a self-adaptive equalizer to have a long impulse response with respect to that of the transmission channel which, taking the speed of transmission into account, requires many coefficients. Now, for stability reasons, the higher the number of coefficients the slower a linear self-adaptive equalizer converges, and to a first approximation the speed of convergence is inversely proportional to the number of coefficients. For this reason, the elimination of phase noise and more generally of any distortion due to rapid variations in the transmission channel is performed by additional correction circuits.
For example, it is known to provide a complex phase shifter after a complex self-adaptive linear equalizer at the receiver end of a digital data transmission using amplitude modulation of two carriers in quadrature. The complex phase shifter is provided with a first order phase-locking loop controlled by the data, however, in the presence of harmonics it is not sufficiently accurate to follow the kind of frequency drift encountered in practice. This has lead to a proposal that a second order phase locking loop should be used controlled by the data, however, this has turned out to be too slow to eliminate phase jitter. This has therefore lead to the use of two successive complex phase-shifters, one having a first order phase-locking loop to eliminate phase jitter, and the other having a second order phase-locking loop to eliminate frequency drift. This results in functions being performed twice over:
The aim of the present invention is to avoid such complication, without thereby reducing the efficiency of phase noise correction.